1. Field of the Invention
The present invention relates generally to material design and, more particularly, to a method and apparatus using an evolutionary algorithm for to optimize crystal structure, including use of metadynamics to avoid the genetic drift.
2. Description of the Related Art
Evolutionary algorithms are widely used in the field of crystal structure prediction. Specifically, evolutionary algorithms are useful to determine a ground state of a crystal structure for a given chemical composition at given pressure and temperature conditions. The ground state refers to the crystal structure with a lowest possible free energy, i.e. enthalpy, for the chemical composition. An evolutionary algorithm of Universal Structure Predictor: Evolutionary Xtallography (USPEX) provides an efficient and reliable method and system for crystal structure prediction, improvements to which are disclosed herein.
USPEX is utilized in various applications, for example prediction of hardness, which is an important property for determination of new materials for applications such as cutting and drilling tools. The ability to predict a hardest phase of a crystal and other structures, for a given stoichiometry, enables a systematic search for novel hard materials and allows efficient evaluation of potentially controversial experimental results. Problems encountered utilizing conventional systems are summarized in Modern Methods of Crystal Structure Prediction, Andriy O. Lyakhov, et al., Wiley VCH (2011). Problems that arise in conventional systems include finding a global minimum on a surface in multidimensional space, such as hardness and free energy, as a function of the atomic positions and lattice vectors, respectively. Computing the hardness of a given crystal structure is a difficult task. Only recently has significant progress been achieved in formulating models that are physically meaningful and sufficiently accurate for several classes of compounds. See, F. Gao et al., Phys. Rev. Lett. 91, 0155021 (2003); A. Simunek et al., Phys. Rev. Lett. 96, 0855011 (2006); K. Li, et al., Phys. Rev. Lett. 100, 235504 (2008); and A. R. Oganov and A. O. Lyakhov, J. Superhard Mater. 32, 143 (2010).
Evolutionary crystal structure prediction begins with a set or population of crystal structures and evolves this set of crystal structures based on input parameters and variation operators that provide the conditions for optimization of the set of crystal structures to produce child crystal structures from parent crystal structures. A conventional method to determine next generations of crystal structures is provided in International Publication No. WO2007/071095 of Glass, et al. Child, i.e., next generation, crystal structures retain vestiges of parent crystal structures after operation of the variation operators, while new features are introduced into the child crystal structures. These new features include both desirable and undesirable characteristics. Variation operators include a heredity operator, which creates a child crystal structure from two or more parents, and a mutation operator, which creates a child using a single parent.
An initial population may be randomly created or input based on desired ground state information, such as likely candidate structures, lattice parameters, and space groups. Conventional evolutionary algorithms locally optimize the crystal structures, typically by relaxation of chemical bonds by a user determined theory, such as empirical potentials, density functional theory, hybrid functions and Quantum Monte Carlo algorithms.
However, conventional evolutionary algorithms generate crystal structures that often become trapped in a local free energy minimum rather than a global free energy minimum. In addition, a number of local minima rises exponentially as the crystal structure's size increases, further raising the risk of trapping. Accordingly, current evolutionary algorithms are limited to crystal structure prediction of materials of only 15-40 atoms in size.
Moreover, random input of conventional systems will often create an initial population of crystal structures that is randomly produced. Such random initialization typically leads to highly disordered output of nearly identical child structures with similar high energies and a low degree of order. Thus, conventional methods and systems fail to provide a method for optimized prediction of crystal structures, particularly for materials with larger sized molecules.